2021 AP exam administration sample student responses AP physics c: electricity and magnetism free response question 1

2021 AP Exam Administration Sample Student Responses AP Physics C Electricity and Magnetism Free Response Question 1 2021 AP ® Physics C Electricity and Magnetism Sample Student Responses and Scoring[.]

Physics C:

Electricity and

Magnetism

Sample Student Responses

and Scoring Commentary

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Inside:

Free Response Question 1

Scoring Guideline

Student Samples

Scoring Commentary

AP® Physics C: Electricity & Magnetism 2021 Scoring Guidelines

© 2021 College Board

Question 1: Free-Response Question 15 points

(a) For an indication that the capacitors act like a short circuit immediately after the switch is

closed

1 100

EQ

R = R = Ω

1 point

For using Ohm’s law to calculate the current through R1

( 100 Ω 10 V )

0.10 A

V I

R I

∆

=

1 point

Total for part (a) 2 points (b) For correctly determining the equivalent resistance during steady-state

R = R + R = Ω + Ω ∴ = Ω

R = R + R = Ω + Ω = Ω

1 point

For correctly calculating the current through the battery

( 120 Ω 10 V )

0.083 A

V I

R I

∆

=

The potential difference across R1

(0.083 A 100 )( ) 8.3 V

V

1 point

(c) i For using a correct equation to calculate the potential difference across C 3

1 point

For using the correct equivalent capacitance of the series combination to calculate the

charge stored in capacitor C 2

10 F 15 F S

C = C + C = µ + µ ∴ = µ

12

1 point

ii For selecting “Greater than” and attempting a relevant justification 1 point

Example response for part (c)(ii)

The potential difference across the series combination of C and 1 C2 is the same as the

potential difference across C3; thus, capacitor C has a greater potential difference 3

across its plates than C2 and has a greater capacitance Because Q C V = ∆ , C3 stores a

greater charge

Scoring note: A justification showing a mathematical proof earns full credit

Total for part (c) 4 points

AP® Physics C: Electricity & Magnetism 2021 Scoring Guidelines

© 2021 College Board

(d) i For indicating that the current through R is zero when the switch is opened 1

1 0

I =

1 point

ii For indicating that the potential difference across R is equal to the potential difference 2

across the capacitors before the switch was opened

1 point

For using Ohm’s law to calculate the current through R2

2

2

1.67 V

30 Ω 0.056 A

R

V I

R I

∆

=

1 point

Total for part (d) 3 points (e) For a curve starting at a nonzero, labeled maximum value 1 point

For a concave-up curve with the horizontal axis as an asymptote 1 point Example response for part (e)

Total for part (e) 2 points (f) For selecting “Below” and attempting a relevant justification 1 point

Example response for part (f)

Because the equivalent capacitance of the circuit would decrease, the time constant would

also decrease Thus the capacitors would discharge more rapidly, and the new curve

would be below the original curve

Total for part (f) 2 points Total for question 1 15 points

E Q1 A 1 of 2

E Q1 A 2 of 2

E Q1 B 1 of 2

E Q1 B 2 of 2

E Q1 C 1 of 2

E Q1 C 2 of 2

AP® Physics C: Electricity and Magnetism 2021 Scoring Commentary

© 2021 College Board

Visit College Board on the web: collegeboard.org

Question 1

Note: Student samples are quoted verbatim and may contain spelling and grammatical errors

Overview

The responses were expected to demonstrate the ability to:

• Identify a short in a circuit

• Recognize that the steady-state current is zero in branches with fully-charged capacitors

• Determine the potential difference across charged capacitors, wired in series and/or in parallel

• Determine the potential difference across a resistor with charge flowing through it and across resistors wired in series and/or in parallel

• Identify equipotentials in a circuit

• Analyze how changes in the overall capacitance affect the time it takes for capacitors to discharge and to model these changes graphically

• Relate the charge stored on a capacitor to its capacitance and the potential difference across it

• Relate the current in a resistor to its resistance and the potential difference across it

Sample: E Q1 A

Score: 13

Part (a) earned 2 points The first point was earned for indicating that the resistance of the circuit at t = 0 is

100 Ω The second point was earned for using Ohm’s law to calculate current Part (b) earned 2 points The first point was earned for determining the equivalent resistance of 120 Ω The second point was earned for calculating the current through the battery to determine the potential difference across R1 Part (c)(i) earned

2 points The first point was earned for using a correct equation to determine the potential difference across C3

or C1,2 The second point was earned for using the equivalent capacitance of C1,2 to determine the charge on C2 Part (c)(ii) earned 2 points The first point was earned for checking “Greater than” and attempting a relevant justification The second point was earned for identifying that ∆V3 > ∆V2, that C3 > C2, and that Q = C∆V Part (d)(i) earned 1 point The point was earned for indicating that the loop containing R1 is now open,

resulting in 0 A in R1 Part (d)(ii) earned 2 points The first point was earned for identifying the correct potential difference across R2 The second point was earned for using 30 Ω to calculate the current through R2 Part (e) earned 2 points The first point was earned for starting the graph on the vertical axis with a labeled maximum value The second point was earned for a concave up curve with the horizontal axis as the asymptote Part (f) earned no points The first point was not earned because “The same” is checked The second point was not earned because any reference to a decreased equivalent capacitance causing the capacitor to discharge more rapidly is omitted

AP® Physics C: Electricity and Magnetism 2021 Scoring Commentary

© 2021 College Board

Visit College Board on the web: collegeboard.org

Question 1 (continued)

Sample: E Q1 B

Score: 8

Part (a) earned 2 points The first point was earned for indicating that the resistance of the circuit at t = 0 is

100 Ω The second point was earned for using Ohm’s law to calculate current Part (b) earned 2 points The first point was earned for determining the equivalent resistance is 120 Ω as implied by the loop rule The second point was earned for calculating the current through the battery to determine the potential difference across R1 Part (c)(i) earned no points The first point was not earned because a reference to the correct

potential difference across C3 or C1,2 is omitted The second point was not earned because the capacitance of

C2 is used to determine the charge on C2 instead of the equivalent capacitance of C1,2 Part (c)(ii) earned

1 point The first point was earned for checking “Greater than” and attempting a relevant justification The second point was not earned because the response uses 10 V across C3 Part (d)(i) earned 1 point The point was earned for indicating that the loop containing R1 is now open, resulting in 0 A in R1 Part (d)(ii) earned no points The first point was not earned because the correct potential difference across the capacitors, just before and just after the switch was opened, is not used The second point was not earned because the resistance of

R2, 30 Ω, is not used to calculate the current Part (e) earned 2 points The first point was earned for starting the graph on the vertical axis with a labeled maximum value The second point was earned for a concave up sketch with the horizontal axis as the asymptote Part (f) earned no points The first point was not earned because the “Above” box is checked The second point was not earned because any reference to the decreased overall capacitance and its effect on the rate of discharge is omitted

Sample: E Q1 C

Score: 2

Part (a) earned 2 points The first point was earned for indicating that the resistance of the circuit at t = 0 is

100 Ω The second point was earned for using Ohm’s law to calculate current Part (b) earned no points The first point was not earned because an incorrect equivalent resistance when the capacitors are fully charged is used The second point was not earned because the response does not include a current calculation to

determine the potential difference across R2 Part (c)(i) earned no points The first point was not earned

because an incorrect value for the potential difference across the branch with C1 and C2 is used The second point was not earned because an incorrect value for the equivalent capacitance is used Part (c)(ii) earned no points The first point was not earned because “Less than” is checked The second point was not earned because the justification omits ∆V3 > ∆V2 Part (d)(i) earned no points The first point was not earned because the response is left blank Part (d)(ii) earned no points The first point was not earned because the response is left blank The second point was not earned because the response is left blank Part (e) earned no points The first point was not earned because the sketch starts at a minimum value The second point was not earned because the curve presented is concave down Part (f) earned no points The first point was not earned because

“The same” is checked The second point was not earned because any reference to the decreased overall capacitance and its effect on the rate of discharge is omitted